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On Supersolvable Groups and a Theorem of Huppert

Published online by Cambridge University Press:  20 November 2018

N. P. Mukherjee  and
Prabir Bhattacharya
N. P. Mukherjee
Affiliation:
Jawaharlal Nehru University, New Delhi, India
Prabir Bhattacharya
Affiliation:
University of Nebraska-Lincoln, Lincoln, NE, U.S.A.
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Abstract

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We obtain the following generalization of a well known result of Huppert. If p is the largest primer divisor of the order of a finite group G and q is any prime distinct from p, then G is supersolvable if and only if every maximal subgroup whose index is relatively prime to either p or q, has prime index.

Keywords

Ftimary 20D1020D25Secondary 20D9920D25solvablesupersolvableFrattini subgroup
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 3 , 01 September 1990 , pp. 314 - 315
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. Huppert, B., Endliche Gruppen I. Springer Verlag, Berlin, 1967.Google Scholar
2. Mukherjee, N. P. and P. Bhattacharya, On the intersection of a class of maximal subgroups of a finite group, Canadian J. Math. 39 (1987), 603–611.Google Scholar
3. Mukherjee, N. P. and P. Bhattacharya, On the intersection of a family of maximal subgroups containing the Sylow subgroups of a finite group. Canadian J. Math. 40 (1988), 352–359.Google Scholar